The biggest question at Manchester United at this time is whether Michael Carrick deserves to be appointed as official head coach or not.
There are many factors that need to be analyzed, from tactics, football philosophy, management style to how Carrick handled the squad he took over after Ruben Amorim.
Carrick always shows calmness, discreetness and tries to maintain stability even in the most chaotic circumstances. That is also the image of Man United under his current leadership.

When Liverpool scored 2 goals in a row at Old Trafford last weekend, Carrick did not rush to the sideline to scream. He still maintained his familiar calm demeanor, continued to closely follow tactical plans and helped the team win a very important 3-2 victory.
Just a few weeks after taking over, Carrick helped Man United defeat a series of direct competitors and bring the team back to the Champions League position. If considering the achievements since he took over, the "Red Devils" are even the team with the most points in the league.
However, there are still many doubts surrounding this former midfielder. A part of the fans believe that Carrick is only creating a short-term effect, similar to Ole Gunnar Solskjaer before. Professional indicators such as ball control, number of chances created or pressing intensity are not really superior to Amorim's final stage.
However, comparing Carrick to Solskjaer is somewhat unfair. If Solskjaer is inclined towards inspiration and mental management, Carrick is a coach who focuses on tactics and control of the match. His philosophy is built on the ability to rotate the ball, short combinations and patience in deploying the ball from the lower line. This is what Carrick has learned when growing up in West Ham's academy.
At Middlesbrough before, Carrick was highly appreciated for his ability to develop young players and build a clear operating system. Players like Hayden Hackney admitted that Carrick is extremely meticulous in every small detail, from his receiving posture to his handling in tight spaces.

Of course, Carrick still has relatively clear limitations. Man United is currently sometimes still unbalanced in midfield, the defense is not really stable and the team still depends quite a lot on Bruno Fernandes' inspiration. However, it cannot be denied that Carrick is helping this team become "leaner", disciplined and significantly more stable.
More importantly, he brings a sense of peace - something that Old Trafford has lacked for many years. Man United does not necessarily need another tactical revolutionary or a coach who likes to make big statements. After many years of chaos, what they need is probably just someone calm enough to get things back on track.